2^9092392+40291 is a probable prime! - Page 4

Jeff Gilchrist · 2011-02-11, 01:35

Also taking: 31, 37, 41, 43

geoff · 2011-02-14, 02:16

Fantastic result! It is great to see a project completed, well done :-)

akruppa · 2011-02-14, 09:57

Did 80 curves at B1=11k, not further factors found.

Edit: P-1 with B1=10^7, B2=10^9, no factor.

Zuzu · 2011-02-14, 13:02

Congrats to all !!!

Lucky, indeed! According to the 2008 paper (Helm et al. in Integers) written when the status was 3 down, 5 to go (compared to Samidoost website dated 2002), the odds at solving the dual Sierpinski problem were 10% at 100M, 50% at 11G and 90% at 72T. Therefore the odds were less than 1% at 9.1M !!! (I think, just 0.9% since the relationship is quasi-linear for small probabilities).

About the future: besides the direct problems (SoB, PSP, extended Sierpinski), are there searches for the prime or extended dual Sierpinski problems?
On my part I have done some personal research and I found that:
- for 78557 < k < 100000, only 2 candidates remain: 79309 (also a direct prime Sierpinski candidate) and 81919, with no PRP for n < 400000
- for k < 100000 there remain some quasi-Sierpinski dual candidates, i.e. with no prime/PRP, except for very small n (such that 2^n < or ~ k), for n < 400000:
90527 (prime for only n=1) ; 56839 and 63859 (prime for only n=2) ; 32899 and 55849 (n=10) ; 85489 (n=14) ; 383 (n=15) ; 24737 (n=17) ; 61969 (n=18).
- for the mixed Sierpinski problem in extended form (neither prime/PRP for k*2^n+1 nor 2^n+k for 78557 < k < 271129), only 2 candidates remain: 79309 (cited above) and 225931 (also a PSP candidate, no PRP for dual, though n has been explored only to 200000).

Cheers to all.

philmoore · 2011-02-15, 00:32

The first two strong probable prime tests are in, with the correct residues, -1 for base 2 and +1 for base 3. I'm pretty certain now that all the other prp tests are going to confirm these, so we have a winner! Congratulations to everyone who has been involved in this project over the past 28 months. I still can't believe it was solved so quickly. Our last find had, I think, about a 17% chance of showing up with the amount of searching done from the previous find, so we were again quite lucky, especially considering that the search could have easily continued for years. So we really do have something to celebrate!

Jeff and Justin, feel free to post any partial results from your strong tests here.

MooMoo2 asked if this project will be archived after double-checking is complete. PrimeGrid has offered to help with the double-checking and we are in the process of creating double-check files for the three unchecked sequences, 2131, 41693, and 40291 using PRPNET. Details will be forthcoming. There is no point in doing any more sieving or P-1 factoring, so that leaves the 20 largest probable primes as the only other piece of this project still unfinished. Certainly the 4 smallest could most likely be proven prime by ECPP with current programs, but two of these numbers are already larger than the largest proven ECPP prime to date, so any of these numbers would require a substantial effort. Perhaps we could just keep a stub open in case anyone wants to reserve one. But yes, most of this project will be archived. I'll go ahead and lock the reservation threads as we get things cleaned up.

Way to go! Thanks to Alex, Ben, Christian, Dmitry, Engracio, Gary, Geoff, Greg, Hadrian, Jayson, Jeff, Justin, Karsten, Kent, Lennart, Luigi, Max, Nathan, Norman, Phil, Robert, Serge, Tim, Winnie, and Yves, all of whom have contributed time either prp testing, sieving, P-1 testing, doing ECPP tests, or some combination. And thanks to the previous collaboration of 2001-2002 that narrowed the list of unfinished sequences down to eight.

Thanks also to George Woltman for the totally efficient prp testing software, to Geoff Reynolds for the awesome sieving software, to Marcel Martin for the contribution of his ECPP software, and to Mike Vang (xyzzy) for hosting a fun home for us.

Batalov · 2011-02-15, 00:49

Cross posting from earlier (inqusitive mids can find this somewhere else):

M.Martin wrote that he was in the process of developing a parallelized 64-bit linux version, and mentioned June-July for a release (things take time).
The threshold of 'possible' will be quantum-leaped right then.

engracio · 2011-02-15, 01:47

Way to go Phil et al , party time.......

enderak · 2011-02-15, 02:13

Great! I believe what's running on my machine now is a duplicate effort... N-1, base 2. Unless I'm mistaken I will just cancel that test.

I look forward to the double-checking!

philmoore · 2011-02-15, 02:55

Justin, I believe that it is also running an N+1 Lucas test as well, and it will choose other bases later, so if you haven't killed the job yet, you could let it run a bit further.

enderak · 2011-02-15, 03:12

Here's what I have so far...

Quote:

Primality testing 2^9092392+40291 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2

and it's only half done. with N-1, hasn't even gotten to the N+1. But if it will be useful to you I will continue to run it.

philmoore · 2011-02-15, 04:11

Thanks. I was tempted to kill my base=2 run originally, but I was not even certain that the script program was correct, or that the version of pfgw I was running would work without errors, so I let it finish to see what was happening. As it turned out, I did have an error in the script program (now corrected), but it would only have made a difference if the number had tested out as composite. I think it would be nice to at least run one strong Lucas test on this number.

2011-02-14, 09:57	#36
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Did 80 curves at B1=11k, not further factors found. Edit: P-1 with B1=10^7, B2=10^9, no factor. Last fiddled with by akruppa on 2011-02-24 at 16:55

2011-02-14, 13:02	#37
Zuzu Sep 2009 13₈ Posts	Five luckily busted !!! Congrats to all !!! Lucky, indeed! According to the 2008 paper (Helm et al. in Integers) written when the status was 3 down, 5 to go (compared to Samidoost website dated 2002), the odds at solving the dual Sierpinski problem were 10% at 100M, 50% at 11G and 90% at 72T. Therefore the odds were less than 1% at 9.1M !!! (I think, just 0.9% since the relationship is quasi-linear for small probabilities). About the future: besides the direct problems (SoB, PSP, extended Sierpinski), are there searches for the prime or extended dual Sierpinski problems? On my part I have done some personal research and I found that: - for 78557 < k < 100000, only 2 candidates remain: 79309 (also a direct prime Sierpinski candidate) and 81919, with no PRP for n < 400000 - for k < 100000 there remain some quasi-Sierpinski dual candidates, i.e. with no prime/PRP, except for very small n (such that 2^n < or ~ k), for n < 400000: 90527 (prime for only n=1) ; 56839 and 63859 (prime for only n=2) ; 32899 and 55849 (n=10) ; 85489 (n=14) ; 383 (n=15) ; 24737 (n=17) ; 61969 (n=18). - for the mixed Sierpinski problem in extended form (neither prime/PRP for k2^n+1 nor 2^n+k for 78557 < k < 271129), only 2 candidates remain: 79309 (cited above) and 225931 (also a PSP candidate, no PRP for dual, though n has been explored only to 200000). Cheers to all. Last fiddled with by Zuzu on 2011-02-14 at 13:30 Reason: Errata on some values*

2011-02-15, 00:32	#38
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 45E₁₆ Posts	We have a winner! The first two strong probable prime tests are in, with the correct residues, -1 for base 2 and +1 for base 3. I'm pretty certain now that all the other prp tests are going to confirm these, so we have a winner! Congratulations to everyone who has been involved in this project over the past 28 months. I still can't believe it was solved so quickly. Our last find had, I think, about a 17% chance of showing up with the amount of searching done from the previous find, so we were again quite lucky, especially considering that the search could have easily continued for years. So we really do have something to celebrate! Jeff and Justin, feel free to post any partial results from your strong tests here. MooMoo2 asked if this project will be archived after double-checking is complete. PrimeGrid has offered to help with the double-checking and we are in the process of creating double-check files for the three unchecked sequences, 2131, 41693, and 40291 using PRPNET. Details will be forthcoming. There is no point in doing any more sieving or P-1 factoring, so that leaves the 20 largest probable primes as the only other piece of this project still unfinished. Certainly the 4 smallest could most likely be proven prime by ECPP with current programs, but two of these numbers are already larger than the largest proven ECPP prime to date, so any of these numbers would require a substantial effort. Perhaps we could just keep a stub open in case anyone wants to reserve one. But yes, most of this project will be archived. I'll go ahead and lock the reservation threads as we get things cleaned up. Way to go! Thanks to Alex, Ben, Christian, Dmitry, Engracio, Gary, Geoff, Greg, Hadrian, Jayson, Jeff, Justin, Karsten, Kent, Lennart, Luigi, Max, Nathan, Norman, Phil, Robert, Serge, Tim, Winnie, and Yves, all of whom have contributed time either prp testing, sieving, P-1 testing, doing ECPP tests, or some combination. And thanks to the previous collaboration of 2001-2002 that narrowed the list of unfinished sequences down to eight. Thanks also to George Woltman for the totally efficient prp testing software, to Geoff Reynolds for the awesome sieving software, to Marcel Martin for the contribution of his ECPP software, and to Mike Vang (xyzzy) for hosting a fun home for us. Last fiddled with by philmoore on 2011-02-16 at 04:37 Reason: added a few more names of contributors - thanks!

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2011-02-11, 01:35	#34
Jeff Gilchrist Jun 2003 Ottawa, Canada 2222₈ Posts	Also taking: 31, 37, 41, 43

2011-02-14, 02:16	#35
geoff Mar 2003 New Zealand 485₁₆ Posts	Fantastic result! It is great to see a project completed, well done :-)

2011-02-15, 00:49	#39
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2²×2,333 Posts	Cross posting from earlier (inqusitive mids can find this somewhere else): M.Martin wrote that he was in the process of developing a parallelized 64-bit linux version, and mentioned June-July for a release (things take time). The threshold of 'possible' will be quantum-leaped right then.

2011-02-15, 01:47	#40
engracio May 2007 11² Posts	Way to go Phil et al , party time.......

2011-02-15, 02:13	#41
enderak Feb 2009 27₁₆ Posts	Great! I believe what's running on my machine now is a duplicate effort... N-1, base 2. Unless I'm mistaken I will just cancel that test. I look forward to the double-checking!

2011-02-15, 02:55	#42
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2·13·43 Posts	Justin, I believe that it is also running an N+1 Lucas test as well, and it will choose other bases later, so if you haven't killed the job yet, you could let it run a bit further.

2011-02-15, 04:11	#44
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2·13·43 Posts	Thanks. I was tempted to kill my base=2 run originally, but I was not even certain that the script program was correct, or that the version of pfgw I was running would work without errors, so I let it finish to see what was happening. As it turned out, I did have an error in the script program (now corrected), but it would only have made a difference if the number had tested out as composite. I think it would be nice to at least run one strong Lucas test on this number.